Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2, x3, such that riữi + x2v2 + x303 = 0.

Orthonormalize the following set of three vectors: {(1, -1, 2), (1, 3, 1), (1, 0, 2)}. Please use legible handwriting and also please explain each step clearly. Thank you!

Let be the vector with initial point (4, 7) and terminal point (8,4). Express as a linear combination of the standard unit vectors. Ov=-3i+47 Ov=-4i +37 Ov=41-37 Ov=4i +3j Ov=-41-3j O None of the above.

Let V₁, V2, V3 be the vectors in R³ defined by 18 ---D V₁ = -6 V2 = -14 V3 = 20 (a) is (V1, V2, Vs} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V₂, and V3 0 (c) Type the dimension of span {V1, V2, V3}: Note: You can earn partial credit on this problem. -25 -18] 0=v₁+√₂+vs (b) Is (v1, vs} linearly Independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁ and V3. 0=v₁+v₁ V3

Explain the Combination of basis vectors.

Please use matrix to solve.

The vectors (-3,4, -1) and (3, -4,1) are orthogonal. True False

Let be the vector with initial point (8, 1) and terminal point (6,5). Express as a linear combination of the standard unit vectors. Ov=4i-2j 05-21-47 Ov=2i+4j Ov=-21-4j Ov=-2+47 O None of the above.

Prove that swapping the order of vectors in the cross product changes the sign of the output: b x a = -(a x b)